The Geometry of Light Echoes and Week 3 Updates

Welcome back, everyone! This week, I would like to do a brief overview of the geometry of the kind of light echo described in the previous post. Buckle up for some math (though not too much)!

Light Echo Geometry

So, the biggest question is how we get meaningful information from a light echo that we have detected. In some cases, it's not necessarily possible, but if an image of the light echo is taken that has sufficient angular resolution to make out the ring, a wealth of information can be obtained. Take a light echo that is observed to have a radius of x pixels.

Not to scale.

Our first task is to find out what x is in some unit of distance in physical space. To accomplish this, we need to know what's called the plate scale of the image - the plate scale tells us the angular size of each pixel in the sky. For example, in the Hubble instrument used to observe our supernova, the plate scale is 0.04 arcseconds per pixel (where 1 arcsecond is 1/3600 of 1 degree). The plate scale tells us the total angular size of the light echo's radius (say, θ). In order to translate this angle into a physical size, we need to know the distance to the supernova's host galaxy (call it D). Using trigonometry, we find the physical size ρ of the light echo to be ρ=D tanθ. Now that we have an idea of the physical size of the light echo, we can use the geometry of the ellipsoid to determine the distance from the supernova explosion to the dust causing the echo. It is a well-known result that

F. Patat, Reflections on Reflexions (2005)

where t is the time elapsed between the supernova being at peak magnitude and the measurement being taken. Using this and our previous relation, we find through routine algebra that the distance z between the supernova and the dust is

This tells us how far away the dust is from the supernova, and thus gives us an idea of what the progenitor system might have been like before the explosion. This also tells us what must happen to a light echo as time passes; in order for z to remain constant as t increases, the quantity tanθ must necessarily increase, which implies that the size of the echo must increase. The ring will become larger as time passes.

If there are multiple dust sheets between the supernova and us, all at different distances, it is possible that light will echo off of each one, resulting in a properly timed image showing a series of concentric rings around the location of the original supernova. Such is the case with famous supernova SN 1987A, one of the best-known examples of a supernova with a light echo.

Anglo-Australian  Telescope photograph by David Malin

It is typically assumed that the progenitor systems of type Ia supernovae are not particularly dusty (i.e., that the dust typically responsible for a light echo is interstellar, and quite far away from the supernova). To show that this is not true would be an interesting insight into how these remarkable phenomena come about.

In some cases, the light echo as imaged is not a ring. In such cases, similar analysis as above can be performed making the same assumption of a sheet in front with allowances made for blurring in imaging or insufficient angular resolution to resolve a ring. Another possibility is that of dust being either behind or in the area immediately surrounding the supernova. If instead of the light rebounding to us off of a sheet of dust in the foreground it gets to us because it rebounds off of a dusty medium in which the supernova is immersed, it may appear as a solid disk rather than a ring when imaged. Through detailed analysis using the image reduction software IRAF, Dr. Milne and I plan to explore the possibility of such circumstellar material around light echoes for which we have data.

Week 3 Updates

In my internship, I have primarily continued to refine the computer simulations of our light echoes. Written in perl, the simulations allow us to compare different models of dust distribution to actual data, (hopefully) allowing us to figure out which one best fits real life. In addition, I have begun to stack more data of our supernovae with the goal of producing a more accurate light curve that can be included in a collaborator's paper. I have also continued my reading of papers and books concerned with both Type Ia supernovae and light echoes. Some of the math is still beyond my reach (some flux calculations in Reflections on Reflexions, for example), but it's definitely coming along!

What Is a Light Echo?

Hello again everyone! Now that I've defined what a type Ia supernova is, I think it would be appropriate to define what a light echo is. This should be a shorter post than the last one. Before we start, I'd like to mention the naming scheme for supernovae. It is fairly simple; they are named by the year they are detected. The first supernova in 2015 will be SN 2015A. The second, SN 2015B and so on. After SN 2015Z, we get SN 2015AA, SN 2015AB, and so on. No distinction is made between supernovae types with this naming scheme.

Light Echoes

As mentioned in my previous post, type Ia supernovae are critical to modern cosmology, and a full understanding of how exactly they come about (i.e., the progenitor systems they arise from) is not currently at hand. Due to their importance, such an understanding is desirable. Analyzing a light echo is one possible method of probing the environment of a supernova's progenitor system.

Based on a diagram by Armin Rest, Harvard University

Above is a diagram of a light echo. Light from the supernova is directed radially outwards, and some of it is directly headed towards Earth (represented as a red arrow on the diagram). This light will reach us first. However, some light that would not initially have been visible from Earth can scatter o ff of interstellar dust (in the diagram, the light blue band is a sheet of interstellar dust) and redirect itself towards us (represented by the blue arrows on the diagram). The longer path length this light travels necessitates that it arrive at Earth at a later time, much as an echo arrives at a later time than the original sound. Surfaces of constant arrival time are traced out by an ellipsoid, which in most cases can be approximated as a paraboloid because the distance between the observer and the supernova is very large (an ellipsoid with one focus approaching infinity). If the dust that scatters the light is a sheet between the supernova and the observer, the echo will take on the appearance of a ring of light around the original supernova. The positioning and size of this ring can be used to discover the distribution of dust around the progenitor system, and thus discern some properties of the progenitor system that would not otherwise be known.

A light echo around V838 Monocerotis. The echo is the brown ring. Courtesy Wikimedia Commons.

Oftentimes telescopes that observe supernova lack the optical resolution to see an actual ring around a light echo. Therefore, we must usually rely on other methods to detect the presence of a light echo. Type Ia supernovae have characteristic ways in which their light fades off. Most commonly, such a fading is shown through a light curve, which plots some measure of luminosity or magnitude versus time.

An example of the light curve of a type Ia supernova. The capital B is the filter. R. Cadonau, 1987.

Because the light that scatters off of the dust arrives at later times, it will often arrive as the supernova itself is fading. This is shown in the light curve as a flattening, as light from the echo overcomes the light from the fading supernova. So, if you have a type Ia supernova with a light curve that flattens out, you might have a light echo on your hands. This is the most common method of detecting light echoes.

Supernovae in General, and Week 1 Updates

While my internship is starting up, I think it might be a good idea to get a few terms out there so the rest of the blog makes sense! The first of these is "supernova".

What Is a Supernova?

In general, the term "supernova" (abbreviated SN) refers to a star exploding. Not all stars do this, but when they do, it's big. Supernova explosions (supernovae, or SNe) are some of the most energetic phenomena in the observable universe. If a supernova were to occur where the sun is now, the amount of radiation and energy your face would receive from looking at it would exceed the amount from a typical nuclear bomb exploding while touching your nose. Stars that go supernova briefly rival the brightness of their host galaxies, expending all their energy in a final violent display. The material left behind in a supernova contains heavier elements than iron, because the high amount of energy present in the explosion is enough to trigger fusion of heavy elements. All elements heavier than nickel were created by supernovae phenomena (except laboratory elements, of course). Supernova remnants (the remains of these violent explosions) are some of the most beautiful visible-light objects in the sky.

The crab nebula, a supernova remnant. Courtesy Wikimedia Commons.

The most well-known kind of supernovae in the public eye are type II supernovae, or core-collapse supernovae. These supernovae occur in very massive stars, between 8 and 50 solar masses. Because of their large mass, these stars can continue the fusion chain past hydrogen and helium, fusing elements in concentric layers until eventually reaching a point where they fuse their cores into iron or nickel.

The onion-like layers of a star about to go supernova. Courtesy Wikimedia Commons.

Fusing iron and nickel provides no net energy output, so pressure from the core is lost and equilibrium is broken. The star is held up through only electron degeneracy pressure. When the mass of the core exceeds the Chandrasekhar limit of about 1.4 solar masses, electron degeneracy pressure gives way to gravity and a catastrophic implosion occurs. The outer core of the star reaches velocities of up to 20% the speed of light, while the inner core reaches temperatures in excess of 100 billion Kelvin. Eventually the star collapses far enough for neutron degeneracy pressure to come into play, and the collapse rebounds and explodes outwards. The core of the star is left behind as either a neutron star (if the star is less than 20 solar masses) or a black hole (if the star is more than 20 solar masses). A neutron star is composed almost entirely of neutrons held up by neutron degeneracy pressure, while a black hole is a singularity.

Although they are interesting, my research does not focus on type II supernovae (as the title of the blog may have hinted). Instead, I'm focusing on the slightly less popularized (but no less interesting!) type Ia supernovae. In general, type I supernovae occur from stars called white dwarfs. When stars on the so-called main sequence (stars like our sun) get very old, they expand to enormous stars called "red giants" before fluffing off their outer layers, leaving behind a tiny, dense ball of electron-degenerate matter called a "white dwarf" (because it is small and white).

The Sirius star system, containing a white dwarf, the faint dot below and to the left of the main star.

White dwarfs do not undergo fusion, and emit radiation because they are hot. Usually, these white dwarfs will simply live out their lives in relative peace, and are expected to eventually cool until they are no longer energetic enough to emit light or heat (becoming so-called "black dwarfs"). Some, however, are destined for a more exciting fate. However, if the white dwarf is in a binary system with another star (like in the above photograph), it's possible for it to end its life in a more spectacular manner. It can pull (or "accrete") mass from its companion star, and if enough mass is gained it will exceed the Chandrasekhar mass (1.44 solar masses, different than the Chandrasekhar limit mentioned above) and they will begin a runaway fusion reaction. Enough energy is released for the star to explode violently in a type Ia supernova.

Type Ia supernovae are particularly important to cosmology because of their uniform nature. They reach a consistent peak luminosity because of the uniformity of the white dwarf progenitor systems. This makes them ideal candidates for so-called "standard candles" that can be used to determine the distances to other galaxies. If a type Ia supernova goes off in NGC 5584, for example, we know what we observe to be it's peak magnitude (or its apparent magnitude), and what its actual (or absolute) magnitude should be, allowing us to calculate the distance to NGC 5584. Such calculations give critical information about the expansion of the universe, making type Ia supernovae critical to the study of the evolution of the universe.

Although type Ia supernovae are very important to modern astronomy, surprisingly little is known for certain about how they come about. The above model of accretion is called the "single degenerate" progenitor model, because it only contains one degenerate star (the white dwarf). Other models such as the double degenerate model propose that two white dwarfs can collide and produce a supernova explosion. Probing the progenitor systems of type Ia supernovae is important in determining how these remarkable events occur.

Internship: Week 1

The first week of my internship has been afflicted with a horrible disease known as "technical difficulty." Data transfer between computers, installing new operating systems, getting licensing for all of the software working, and finding out we don't have all the data we thought we had have all been problems encountered thus far. Despite these setbacks, much work has been done and much progress made. I have done considerable reading from the theses of two of Dr. Milne's graduate students, Dina Drozdov and Ginger Bryngelson, and read through several papers on previous light echoes in type Ia supernovae. Additionally, I have done work on refining and improving the computer simulations of the light echo in our 2007 supernova, with the goal of better understanding the geometry of dust around the progenitor system.

Welcome!

Hi everyone! Welcome to my blog. The subject matter should be pretty obvious - I'll be discussing and cataloging my work on my Senior Research Project (SRP).

I will be assisting Dr. Peter Milne at the University of Arizona's Steward Observatory in examining the data (and the conclusions that can be drawn from it) from light echoes around two recent type Ia supernovae. The work will focus mainly on determining two things: first, whether the echoes were formed by sheets of dust in interstellar space or by dust clouds immediately surrounding the progenitor system; and second, what the results of the first question can tell us about the environment and evolution of the progenitor system.

I hope you enjoy reading about my journey!